[Nexus 7 (2013) Q&A] 459below:
So I'm giving up. I'm going to look for a replacement motherboard and try to construct a shabby 64 GB USB-Stick. The pads were probably torn almost right after I have removed the eMMC and tried to clean the pads on the motherboard. Unfortunately I skipped on the flux the first time when using the solder wick and it got stuck on the pads. I haven't realized it until I soldered the new eMMC onto the board. Judging by the way the pads had solder attached, It really would've worked, if I hadn't destroyed the board a few weeks prior. Well in any case... This is what MiFlash will respond with, if the eMMC isn't connected at all:

[00001C64]CreateManagedObject(1273): Unspecified error(0x80131604)
[00001C64]GetFactoryObject(1317): Unspecified error(0x80131604)
[00001C64]CreateManagedObject(1273): Unspecified error(0x80131604)
[00001C64]GetFactoryObject(1317): Unspecified error(0x80131604)
[00001C64]GetFactoryObject(1338): The specified service does not exist.(0x800704db)
[00001C64]GetSearchPath(1393): The specified service does not exist.(0x800704db)
[000024AC]CEmergencyFlasher::IsQPSTServer(634): Not implemented(0x80004001)
[000024AC]COM6	0.06	Load programmer "C:\Users\459below\Desktop\nexus7_debrick\ME571KL-OPEN_epad-eng-800M-xhdpi-hdpi-D00_1.15.F_0610-10.10.0.51.1.19-20131230-1921-Rawdata.edited\MPRG8064.hex"
[000024AC]COM6	0.08	Open serial port "\\.\COM6"
[000024AC]COM6	0.08	Send parameters command
[000024AC]COM6	0.08	Write and verify address 0x2a000000, size 59372
[000024AC]COM6	0.33	Jump to flash programmer(0x2a000000)
[000024AC]COM6	0.48	Open boot file "C:\Users\459below\Desktop\nexus7_debrick\ME571KL-OPEN_epad-eng-800M-xhdpi-hdpi-D00_1.15.F_0610-10.10.0.51.1.19-20131230-1921-Rawdata.edited\8064_msimage.mbn"
[000024AC]COM6	0.48	Open serial port "\\.\COM6"
[000024AC]COM6	1.39	Send hello command 0
[000024AC]ReadRobust(198): Access is denied.(0x80070005)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReadRobust(198): Reached the end of the file.(0x80070026)
[000024AC]ReceivePacket(455): Reached the end of the file.(0x80070026)
[000024AC]DownloadMiniKernel(887): Reached the end of the file.(0x80070026)
[000024AC]COM6	3.30	Send hello command 1
[000024AC]COM6	3.33	Enable trusted security mode
[000024AC]COM6	3.33	Open EMMC card USER partition
[000024AC]log: Open multi failed, unknown error
e•
[000024AC]err: Open multi failed, unknown errorÿ¼(7340111)
[000024AC]DownloadMiniKernel(940): Catastrophic failure(0x8000ffff)
[000024AC]CSoftwareDownload::DownloadBySettings(2615): Catastrophic failure(0x8000ffff)
[000024AC]COM6	3.34	Open serial port "\\.\COM6"
[000024AC]COM6	3.34	Send configure command
[000024AC]COM6	3.34	Send nop command
[000024AC]COM6	3.34	Max buffer sector is 0
[000024AC]COM6	3.34	Open program file "C:\Users\459below\Desktop\nexus7_debrick\ME571KL-OPEN_epad-eng-800M-xhdpi-hdpi-D00_1.15.F_0610-10.10.0.51.1.19-20131230-1921-Rawdata.edited\rawprogram0.xml"
[000024AC]COM6	3.34	Writing file "C:\Users\459below\Desktop\nexus7_debrick\ME571KL-OPEN_epad-eng-800M-xhdpi-hdpi-D00_1.15.F_0610-10.10.0.51.1.19-20131230-1921-Rawdata.edited\radio.img" to partition at 131072
[000024AC]COM6	3.34	WriteFile position 0000000000000000, size 0
[000024AC]COM6	3.34	WriteFile position 0000000000000000, size 0
[000024AC]COM6	3.34	WriteFile position 0000000000000000, size 0

That is the same which it responded, when the eMMC was partially connected.

So this will probably be it for me. It was fun! And thanks for all the pointers.

/edit

The 64 GB eMMC is fine. I already mirrored the old eMMC onto this and increased the partition size of user data.

[ 1083.685149] usb-storage 3-10.4.2:1.0: USB Mass Storage device detected
[ 1083.685529] scsi host8: usb-storage 3-10.4.2:1.0
[ 1084.704035] scsi 8:0:0:0: Direct-Access Multiple Card Reader 1.00 PQ: 0 ANSI: 0
[ 1084.704368] sd 8:0:0:0: Attached scsi generic sg6 type 0
[ 1084.953073] sd 8:0:0:0: [sdg] 122159104 512-byte logical blocks: (62.5 GB/58.3 GiB)
[ 1084.953408] sd 8:0:0:0: [sdg] Write Protect is off
[ 1084.953411] sd 8:0:0:0: [sdg] Mode Sense: 03 00 00 00
[ 1084.953747] sd 8:0:0:0: [sdg] No Caching mode page found
[ 1084.953750] sd 8:0:0:0: [sdg] Assuming drive cache: write through
[ 1084.959052] sd 8:0:0:0: [sdg] Attached SCSI removable disk

So I've ordered a new motherboard on eBay. Judging by the description, maybe it also suffers from an eMMC issue. But since it's eBay, it might be an old potato chip with "Nexus" written on it. I figured I might as well trow another 12 € at this, before I resign.